Determining the third point on an isosceles triangle

Given the x/y values of the two points on the base, and the length of the altitude -- or 'height' -- of the triangle, is it possible to determine the x,y value of the third point? Thanks in advance for any ideas.

Ok, I suppose I need to elaborate...what would the process be to determine the x/y value of the third point? I read somewhere about finding the midpoint and then using a unit vector, but I'm not clear on how that would look (if that's a viable solution)

Thanks, Soroban -- this is exactly what I was looking for. I had thought that there would be two possible points, but from playing around with your formula, it seems that this is determined by whether the value of h is positive or negative. Anyways, I've been able to integrate this solution into a program I'm working on and it's working as desired, so I appreciate the time you spent.